Cotton cost has always been the single major contributor to the cost of gray yarns. Consequently, economic cotton selection for meeting yarn specifications continues to be one of the main concerns of a spinner. Left to himself, any spinner would very much like to spin a sample of every single lot of cotton to yarn before taking the decision to buy the lot or not. However, the exigency of the situation rules out this most reliable basis for cotton selection. One has mostly to take decisions on the purchase of cotton on the basis of test reports.

In reading meaning out of test reports of the cotton under consideration, one has often mentally to balance the shortfall in one characteristic with the premium in another characteristic. Let us consider, for example, the two cottons in Table - I – 1 - i. Cotton ZZ is shorter and coarser, but stronger than cotton XX. Which of the two cottons would be appropriate to spin 15 tex (NE 40) hosiery yarn? Again which of the two would be appropriate for 20 tex (NE 30) warp yarn? In order to answer these questions we need to be able to complete the table by writing in the estimated tenacity of each yarn of specified count and twist from each of the two cottons. Over the years research workers have, therefore, expended considerable effort on the derivation of equations for the estimation of yarn tenacity from cotton fibre characteristics.

Most available equations can only be used to estimate CSP of yarns spun at the optimum twist. Very few equations aim at predicting CSP of yarns at a range of twists. All these equations suffer from one or both of two shortcomings: in spite of an impressive value of correlation coefficient, large errors in individual estimates of CSP, even consistent bias in the case of some cottons; not contributing to our understanding of the specific manner in which fibre-length and fibre-fineness influence the translation of fibre-tenacity to yarn tenacity. A review of two recent CSP equations will clarify the point.

In 2002 Chellamani, Thanabal, Basu and Ratnam (4) proposed a fibre quality index formulated out of HVI cotton test data:

Let us recall a pet sum of our middle-school arithmetic teachers. Chidambaram invested Rs.1000 at simple interest of 10% payable with the principal at the end of six years. Rashiklal invested Rs.1000 at interest of 8% accruable half-yearly for a period of six years. Who will get more money at end of six years?

Would you want the second formula to be free of the power function just for the sake of simplicity? There is an important message for us here.

Legitimately therefore, we expect two things from any yarn tenacity equation: i) estimates of acceptable accuracy; ii) elucidation of how fibre-length and fibre fineness govern the contributions of yarn irregularity and twist to yarn tenacity. Neither the structure of Neelakantan’s equation, nor the expressions for k, t, and d stand any such meaningful interpretation. Each of these expressions is a medley of all available fibre characteristics churned out by the computer when programmed to minimize the error of prediction. Consequently Neelakantan’s model incurs Morton’s criticism (4), that it ‘does nothing to advance our understanding—indeed, it tends to obscure the issue—of how fibre properties determine spinning behaviour’

Once again we see the need for a meaningful CSP equation.